Our app publishes by Collection, so what you can do is head to the Settings within the app, and then choose which Collection to publish:
You can always remove the products individually from Google Merchant Center as well, and that may be easier depending on how many items you have. :)
Hope that helps!
I would appriciate if you could tell me how the feed is built as of the following conditions
Is the Rule of unavailbility is "stronger" than the availbility?
Is the product is avilable on Google Merchant's feed?